PSI - Issue 4

Hans-Jakob Schindler / Procedia Structural Integrity 4 (2017) 48–55 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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2

defined loading conditions. Often the calculated residual life is shorter than the one measured in component testing or full-sized experiments (Luke et al. (2011), Beretta and Carboni (2011)). In a real axle in service, where the initial crack size is poorly known, loading sequence and amplitudes are stochastic and environmental effects may interfere, an accurate safe life prediction is even more difficult and affected by uncertainties. There are two key influencing factors that affect the fatigue growth behavior of a crack and complicate transferability of crack-growth rates from test specimens to the real axle: One is crack-closure that reduces the effective loading range of the crack, and the other are stationary pre-stresses such as residual stresses and the stresses due to the press-fit of the wheels. The corresponding effects are demonstrated by typical examples in this paper. Residual stresses are present in nearly any component made of steel. In general, they only affect the mean stress as characterized by the stress ratio R. Therefore, they have a significant influence on the endurance limit in case of a sharp notch or crack-like defects (Schindler et al. (2007)), but only a relatively small one on crack initiation at a smooth surface and on the growth rate of a crack. However, for R < 0 as in the case of rotating bending, a shift in the mean stress causes a change of the effective range of the stress intensity factor (SIF) K I because of crack closure. In order to account for the residual stresses in a safe life analysis the SIF due to them should be known, which requires knowledge of the residual stress profile up to the critical size of the crack. Measuring residual stress profiles is not an easy task. A suitable method for this purpose is the cut-compliance method (CC-method) as proposed by Schindler (1997) and Schindler, Cheng and Finnie (1997). In the present paper, the CC-method and its application to determine the residual stress profile in a railway axle is briefly described. The effect of the measured residual stresses on the calculated residual life is shown by an example.

2. Theoretical Considerations

Modified to account for the threshold behaviour of fatigue crack growth, Paris’ law in its simplest form reads as

dN da



 ( )

(1)

( ) C R K K R n    

n th



where  K = K max - K min denotes the range of K I due to the load cycles and  K th the fatigue crack threshold. C and n are fitting constants. C as well as  K th depend significantly on the stress-ratio R = K min /K max . If the crack is growing through a field of residual stresses, the stress component perpendicular to the crack is released to zero at the crack-faces, which causes a re-distribution of the original stress-field in the surrounding of the crack. In particular, it gives rise to an additional stress intensity at the crack-tip, denoted in the following as K Irs . The latter adds to K I due to the external load, so the loading parameters  K and R in (1) are obtained as

 

(2)

K K K K K R K K     min min max ;

rs

rs

max

Note that  K is not affected by the residual stress. Crack closure plays an important role in fatigue crack growth, since it shields the crack-tip from feeling the entire range of  K as imposed by the external loads. It is suitable to distinguish between two components of crack closure: On the one hand, remote closure that originates from contact of the crack-faces remote from the crack-tip, where no more plastic deformation occurs under compressive stresses during further crack growth. On the other hand, as pointed out by Elber (1971), there is the phenomenon of plasticity-induced closure in the vicinity of the crack-tip. The latter is an inherent part of the micromechanics of fatigue damage at the crack-tip, which are the main reason for crack retardation after overloads. These two types of crack closure are related to each other, so they cannot be distinguished easily. Nevertheless, in the following only remote closure is considered conceptually, which for the sake of simplicity is assumed to depend only on extrinsic effects such as corrosion and roughness of the crack faces, but not on the interrelation with plasticity-induced local crack-closure. In the following, K rem is introduced as the minimum K I that a surface crack in a railway axle can experience due to remote closure, meaning that for K I < K rem , the stresses are transmitted across the crack plane by full contact of